A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 2.15 × 104 m/s (Va) and the radius of the orbit is 5.15 × 106 m (ra). A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.65 × 106 m (rb). What is the orbital speed (Vb) of the second satellite
I set it up as (Va)^2/ra=(Vb)^2/rb then plugged in the given values and solved and got 3.22x10^-3 as my answer. Am I correct?
To solve this problem, you used the conservation of angular momentum for circular orbits. According to this principle, the angular momentum remains constant for an object in a circular orbit.
The formula you used is correct:
(Va)^2/ra = (Vb)^2/rb
Where Va is the orbital speed of the first satellite, ra is the radius of its orbit, Vb is the unknown orbital speed of the second satellite, and rb is the radius of its orbit.
You plugged in the given values:
(Va)^2 = (2.15 × 10^4 m/s)^2
ra = 5.15 × 10^6 m
rb = 8.65 × 10^6 m
After substituting these values into the equation, you can solve for Vb:
(2.15 × 10^4 m/s)^2 / (5.15 × 10^6 m) = (Vb)^2 / (8.65 × 10^6 m)
Now, let's calculate the result:
(Vb)^2 = (2.15 × 10^4 m/s)^2 * (8.65 × 10^6 m) / (5.15 × 10^6 m)
(Vb)^2 = 4.62275 × 10^12 m^2/s^2
Vb = √(4.62275 × 10^12 m^2/s^2)
Vb = 6.80 × 10^6 m/s
So, the orbital speed of the second satellite (Vb) is approximately 6.80 × 10^6 m/s. Therefore, your answer of 3.22 × 10^-3 is incorrect.